Boolean algebra (structure)

Note, however, that the absorption law and even the associativity law can be excluded from the set of axioms as they can be derived from the other axioms (see Proven properties).

It follows from the last three pairs of axioms above (identity, distributivity and complements), or from the absorption axiom, that

The first four pairs of axioms constitute a definition of a bounded lattice.

It follows from the first five pairs of axioms that any complement is unique.

Herbert Robbins immediately asked: If the Huntington equation is replaced with its dual, to wit:

Further work has been done for reducing the number of axioms; see Minimal axioms for Boolean algebra.